We theoretically investigate the controlled dynamic polarization of lattice nuclear spins in GaAs double quantum dots containing two electrons. Three regimes of long-term dynamics are identiﬁed, including the buildup of a large difference in the Overhauser ﬁelds across the dots, the saturation of the nuclear polarization process associated with formation of so-called ‘‘dark states’’, and the elimination of the difference ﬁeld. We show that in the case of unequal dots, buildup of difference ﬁelds generally accompanies the nuclear polarization process, whereas for nearly identical dots, buildup of difference ﬁelds competes with polarization saturation in dark states. The elimination of the difference ﬁeld does not, in general, correspond to a stable steady state of the polarization process.